1 Answer
1

If $V\sim \chi^2(7)$ and $F$ denotes its distribution function, i.e. $F(v)=P(V\leq v)$, then these values express that $F(1.239)=0.01, F(2.167)=0.05,\ldots, F(18.58)=0.99$. Using this we can obtain
$$
P(1.239&ltV\leq 18.48)=P(V\leq 18.48)-P(V\leq 1.239)=F(18.58)-F(1.239)=0.98.
$$
And then
$$
P(V\notin (1.239,18.48])=1-0.98=0.02
$$
as you claimed.